An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality
Gerard E. Dallal, Leland Wilkinson · The American Statistician · 1986
Table 1 corrects the critical values for testing normality reported by Lilliefors (1967). The corrected table allows us to derive a simple analytic approximation to the upper tail probabilities of his test statistic for probabilities less than .10. With few exceptions, the approximation is more accurate than Lilliefors's original table.